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SEMI MF1392-1103 © SEMI 2003 15 15 Keywords 15.1 capacitance-voltage method; carrier density; carrier density profile; depth profile; epitaxial wafers; mercury prob e; net carrier densi ty; polishe d wafers; profiles; re…
SEMI MF1392-1103 © SEMI 2003 14
m = number of individual values of net carrier den-
sity to be averaged (see Section 12.5.1),
k = whole number such that C
i+k
is between 80 and
85% of C
i
,
n = number of capacitance-voltage pairs measured,
and
N
i
=
net carrier density, cm
−3
, corresponding to each
average depth, W'
i
.
12.5.3 Calculate the sample standard deviation of the
net carrier density as follows:
∑
=
−
−
=
m
i
avgi
NN
m
s
1
2
)(
1
1
(21)
12.6 If the test wafer is not homogeneously doped or if
s exceeds 10% of N
avg
, plot the net carrier density
profile as a graph of N
i
as a function of W
i
.
NOTE 19: Related Information 3 describes composition of
the numerical constants used in the above calculations.
13 Report
13.1 Report the following information:
13.1.1 Type and model number of instrumentation used
including software type and revision, if a computer
controlled system is employed,
13.1.2 Probe configuration used,
13.1.3 Operator identification,
13.1.4 Date of measurement,
13.1.5 Lot number and test specimen identification
including conductivity type and surface orientation,
13.1.6 Wafer and sampling plan, if applicable,
13.1.7 Compensation capacitance, pF, as determined in
Section 10.2,
13.1.8 Method of calculation used, and
13.1.9 Average net carrier density, N
avg
, and sample
standard deviation, s, or net carrier density profile (plot
of N
i
as a function of W
i
), as determined in Section
12.5.
13.2 For referee measurements, also report the
following:
13.2.1 Mercury probe contact area, A
eff
, cm
2
, as
determined in Section 10.3.4,
13.2.2 Forward resistance at 1 V bias or equivalent
series resistance, Ω, as determined in Section 11.4,
13.2.3 Phase angle, degrees, as determined in Section
11.4.2.4, if measured,
13.2.4 Maximum applied reverse bias voltage, V, as
determined in Section 11.5,
13.2.5 Maximum leakage current density, J
r
, mA/cm
2
,
as determined in Section 11.5,
13.2.6 Surface treatment used, if applicable, and
13.2.7 Other data as tabulated in a data sheet
appropriate to the calculation method used.
14 Precision and Bias
14.1 Repeatability — The within-laboratory precision
achievable with this test method was estimated from
the results of several experiments. In the first
experiment, ten nominally 50 Ω·cm n-type wafers were
measured on two days by two different operators using
a single instrument. The pooled coefficient of variation
was 0.183%; the largest observed coefficient of
variation was 0.35%.
14.1.1 Based on the pooled value, the repeatability, r,
is estimated to be about 0.51%. In the second
experiment, ten nominally 1 Ω·cm n-type wafers were
measured three times on a single instrument by a single
operator. The wafer surfaces were treated prior to each
measurement. The pooled coefficient of variation was
0.493%; based on this value the repeatability, r, is
estimated to be about 1.37%.
14.2 Reproducibility — The reproducibility of this test
method has not been evaluated because of difficulties in
establishing and applying a common specimen surface
preparation for use in a round robin to evaluate
reproducibility. No such tests are planned.
14.3 Calculations of the errors in net carrier density, N
i
,
and depletion depth, W
i
, expected on the basis of the
precision requirements of the various parameters
measured in the test procedure could, in principle, be
made in accordance with the procedures of Practice
D 4356. However, because the formulas include ratios
of differences of both capacitance and voltage and
because the voltage and capacitance are coupled, these
errors depend both on the intervals chosen in the
experiment and on the physical characteristics of the
test specimen. The calculation procedure for the
incremental method included in this test method uses
large intervals in order to minimize the errors from the
use of finite intervals for the determination. For some
examples of the effect of both random errors and finite
interval errors on the calculated value of net carrier
density, N
i
.
9
14.4 Bias — The bias of this test method cannot be
evaluated because there are no available reference
standards suitable for evaluating bias.
SEMI MF1392-1103 © SEMI 2003 15
15 Keywords
15.1 capacitance-voltage method; carrier density;
carrier density profile; depth profile; epitaxial wafers;
mercury probe; net carrier density; polished wafers;
profiles; resistivity; silicon; single crystal silicon
SEMI MF1392-1103 © SEMI 2003 16
RELATED INFORMATION 1
RECOMMENDED WAFER SURFACE TREATMENTS
NOTICE: This related information is not an official part of SEMI MF1392. It was developed during the original
development of the document. This related information was approved for publication by full letter ballot on July 12,
2003.
R1-1.1 The following surface treatments have been
found to result in satisfactory surfaces under a variety
of conditions and are recommended for use in
connection with this test method. Other surface
treatments may also be satisfactory and may be used if
agreed upon between the parties to the test.
R1-1.2 Place the wafer to be treated in a center slot of a
hydrofluoric acid cassette.
R1-1.3 Dip in HF for 30 s (concentrated HF) or 5 min
(dilute HF).
R1-1.4 Rinse in water for 10 min.
R1-1.5 For p-type wafers, spin dry in an air
atmosphere. If subsequent measurements are unstable,
heat treat the wafer for 30 min at 120 ± 10° C in air.
R1-1.6 For n-type wafers, transfer the wafer
immediately from the hydrofluoric acid cassette to a
center slot of a hydrogen peroxide cassette (Caution—
see Note 1), and continue with the following:
R1-1.6.1 Immerse in 15% H
2
O
2
for 10 min at 70° to
90° C.
R1-1.6.2 Rinse in water for 2 min.
R1-1.6.3 Spin dry in an air atmosphere (Note 1).
NOTE 1: Alternatively, the wafers may be dried by blow
drying with a filtered nitrogen blow-off gun while holding the
wafer at a 45° angle with the lower edge of the wafer resting
on a clean-room wipe.